Group in which every normal subgroup is finite or has finite index

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

Definition

A group in which every normal subgroup is finite or has finite index is a group in which every normal subgroup satisfies one of these two conditions: either it is a finite group (and hence a finite normal subgroup), or it is a normal subgroup of finite index in the whole group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
simple group
finite group
group in which every nontrivial normal subgroup has finite index